SCIENTIFIC PROGRAMS AND ACTIVITIES

October 22, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES


Held at the University of Ottawa
Room B005 KED Building, 585 King Edward (map)

Organizers: Vladimir Chernousov (Alberta) and Kirill Zainoulline (Ottawa)
Local organizer committee: Caroline Junkins, Kirill Zainoulline
OVERVIEW

In the last 10-15 years the theory of linear algebraic groups has witnessed an intrusion of the cohomological methods of modern algebraic geometry and algebraic topology. These new methods have led to breakthroughs on a number of classical problems in algebra, which are beyond the reach of earlier purely algebraic techniques. The workshop will focus at the following new emerging techniques and applications:

- The proof of the Grothendieck-Serre conjecture based on the theory of affine Grassmannians.
The Grothendieck-Serre conjecture stated in 60's says that any rationally trivial G-bundle is locally trivial (in Zariski topology), where G is a smooth reductive group scheme over a local regular ring. In a recent preprint (Nov. 2012) Fedorov and Panin proved the conjecture in the geometric case using new connections with the theory of affine Grassmannians.

- Computation of generalized equivariant cohomology of projective homogeneous and toric varieties.
The notion of an algebraic oriented cohomology theory was introduced and extensively studied during the last decade by Levine, Morel, Panin, Smirnov and others. The universal such theory called algebraic cobordism has many applications in the theory of quadratic forms and homogeneous spaces. Its equivariant version is believed to contain all the information concerning cohomological behaviour of homogeneous spaces. In particular, its computation can lead to a better understanding of cohomology and related combinatorics of toric varieties.

OUTLINE OF THE PROGRAM

The workshop will run for three full days and a morning session during the fourth day (Friday morning - Monday noon) and will feature a unique combination of two introductory mini-courses and research-level talks. The two mini-courses will have three 80 min. lectures each and directed towards PhD students and young researchers. The topics are the following.
(a) Toric varieties and equivariant cohomology by Kalle Karu, University of British Columbia
- The course will be an introduction to toric varieties and equivariant cohomology.

(b) Introduction to principal homogeneous spaces by Roman Fedorov, Kansas State University
- The course will be devoted to the basics in the theory of torsors and the Grothendieck-Serre conjecture.

Besides the two mini-courses, there will be invited one-hour talks by the leading experts in the area, as well as short talks by young researchers, postdocs and graduate students.

INVITED SPEAKERS

Alex Duncan, University of Michigan
Stefan Gille, University of Alberta
Nikita Karpenko, University of Alberta
Daniel Krashen, University of Georgia
Nicole Lemire, Western University
Alexander Merkurjev, University of California at Los-Angeles
Julia Pevtsova, University of Washington
Andrei Rapinchuk, University of Virginia
Zinovy Reichstein, University of British Columbia

Schedule of the workshop (speakers abstracts)

Friday, May 23
9:00-10:20 Course I - Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces
10:20-10:40 Coffee
10:40-12:00 Course II - Kalle Karu (UBC)
Toric varieties and equivariant cohomology
12:00-13:30 Lunch
13:30-14:20 Alexander Merkurjev (UCLA)
Motivic decomposition of of certain group varieties
14:30-15:20 Zinovy Reichstein (UBC)
An invariant of a representation of a finite group
15:30-16:20 Andrei Rapinchuk (University of Virginia)
On algebraic groups with the same tori (joint work with V. Chernousov and I. Rapinchuk)
16:30-16:55 Igor Rapinchuk (Harvard University)
The genus of a division algebra
17:00-17:25 Alexander Neshitov (Steklov Institute/Ottawa)
Invariants of degree 3 and torsion on Chow group of a versal flag.
Saturday, May 24
9:00-10:20 Course II - Kalle Karu (UBC)
Toric varieties and equivariant cohomology
10:20-10:40 Coffee
10:40-12:00 Course I - Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces
12:00-13:30 Lunch
13:30-14:20

Nikita Karpenko (Alberta)
Incompressibility of Weil transfer of generalized Severi-Brauer varieties

14:30-15:20 Julia Pevtsova (University of Washington)
Supports and tensor ideals for finite group schemes.
15:30-15:55 Mathieu Huruguen (UBC)
Special reductive groups over an arbitrary field
Sunday, May 25
  Free morning
13:30-14:50 Course I - Roman Fedorov (Kansas State)
Introduction to principal homogeneous spaces
15:00 -16:20 Course II - Kalle Karu (UBC)
Toric varieties and equivariant cohomology
16:30-16:55 Uladzimir Yahorau (Alberta)
Conjugacy theorem for extended affine Lie algebras
17:00-17:25 Changlong Zhong (Alberta)
Equivariant cohomology and formal Demazure algebra
17:30-17:55 Wanshun Wong (Ottawa)
Formal group rings of toric varieties
Monday, May 26
9:00-9:50 Nicole Lemire (Western)
Four-dimensional algebraic tori
9:50-10:10 Coffee
10:10-11:00 Daniel Krashen
TBA
11:10-12:00 Alexander Duncan (Michigan)
Twisted Forms of Toric Varieties
12:10-13:00 Stefan Gille (Alberta)
Geometrically rational surfaces with 0-dimensional motives
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May 27, 2014, 73rd Algebra Day

Participants may also be interested in a closely related event, the 73rd Algebra Day on May 27, 2014, at the University of Ottawa.
(organizer: Hadi Salmasian, room B005, KED)

9:30 Siddhartha Sahi (Rutgers University)
TBA

11:00 Arturo Pianzola (University of Alberta)
Non-abelian cohomology and infinite dimensional Lie theory (suite)

14:00 Michel Waldschmidt (Université Paris VI)
Three algebras arising from Multiple Zeta Values

Confirmed Participants as of May 12th

Full Name University/Affiliation
Bardestani, Mohammad University of Ottawa
Bose, Anirban Indian Statistical Institute
Bumagin, Inna Carleton University
Chernousov, Vladimir University of Alberta
Christie, Aaron University of Ottawa
Duncan, Alexander University of Michigan
Fedorov, Roman Max Planck Institute Bonn
Gille, Stefan University of Alberta
Huruguen, Mathieu UBC
Junkins, Caroline University of Ottawa
Karpenko, Nikita University of Alberta
Karu, Kalle University of British Columbia
Krashen, Daniel University of Georgia
Leclerc, Marc-Antoine University of Ottawa
Lemay, Joel University of Ottawa
Lemire, Nicole Western University
Lemire, Nicole Western University
Lu, Haoye University of Ottawa
Merkurjev, Alexander University of California, Los Angeles
Neher, Erhard University of Ottawa
Neshitov, Alexander University of Ottawa
Nevins, Monica University of Ottawa
Pevtsova, Julia University of Washington
Pianzola, Arturo University of Alberta
Polak, Jason McGill University
Rapinchuk, Andrei University of Virginia
Rapinchuk, Igor Harvard University
Reichstein, Zinovy University of British Columbia
Salmasian, Hadi University of Ottawa
Sarkar, Soumen University of Regina
Savage, Alistair University of Ottawa
Wong, Wanshun University of Ottawa
Yahorau, Uladzimir University of Alberta
Zainoulline, Kirill University of Ottawa
Zhong, Changlong University of Alberta


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